




class 		_A   :






  def __init__(    self						:      Optional[Any] ,		_A						:      Tuple ,		_A						:      List[Any] ,		_A						:      Any )						->       Optional[Any]:






       """simple docstring"""







       lowercase   :  Union[str, Any]        =					None
       lowercase   :  Union[str, Any]        =					None
       lowercase   :  Optional[int]        =					graph

       self._normalize_graph(_A ,		_A )
       lowercase   :  Dict        =					len(_A )
       lowercase   :  Any        =					None






  def    __a     (    self						:      Any ,		_A						:      List[str] ,		_A						:      int )						->       str:






       """simple docstring"""







       if sources is int:
            lowercase   :  Optional[int]        =					[sources]
       if sinks is int:
            lowercase   :  Any        =					[sinks]

       if len(_A ) == 0 or len(_A ) == 0:
            return

       lowercase   :  Optional[Any]        =					sources[0]
       lowercase   :  int        =					sinks[0]

       # make fake vertex if there are more
       # than one source or sink
       if len(_A ) > 1 or len(_A ) > 1:
            lowercase   :  Optional[Any]        =					0
            for i in sources:
                 max_input_flow += sum(self.graph[i] )

            lowercase   :  Dict        =					len(self.graph ) + 1
            for room in self.graph:
                 room.insert(0 ,		0 )
            self.graph.insert(0 ,		[0] * size )
            for i in sources:
                 lowercase   :  List[str]        =					max_input_flow
            lowercase   :  Optional[Any]        =					0

            lowercase   :  Dict        =					len(self.graph ) + 1
            for room in self.graph:
                 room.append(0 )
            self.graph.append([0] * size )
            for i in sinks:
                 lowercase   :  Any        =					max_input_flow
            lowercase   :  Optional[int]        =					size - 1






  def    __a     (    self						:      List[Any] )						->       Any:






       """simple docstring"""







       if self.maximum_flow_algorithm is None:
            raise Exception('''You need to set maximum flow algorithm before.''' )
       if self.source_index is None or self.sink_index is None:
            return 0

       self.maximum_flow_algorithm.execute()
       return self.maximum_flow_algorithm.getMaximumFlow()






  def    __a     (    self						:      Optional[int] ,		_A						:      List[Any] )						->       Union[str, Any]:






       """simple docstring"""







       lowercase   :  str        =					algorithm(self )


class 		_A   :






  def __init__(    self						:      Union[str, Any] ,		_A						:      List[Any] )						->       Union[str, Any]:






       """simple docstring"""







       lowercase   :  Union[str, Any]        =					flow_network
       lowercase   :  Tuple        =					flow_network.verticesCount
       lowercase   :  List[Any]        =					flow_network.sourceIndex
       lowercase   :  Union[str, Any]        =					flow_network.sinkIndex
       # it's just a reference, so you shouldn't change
       # it in your algorithms, use deep copy before doing that
       lowercase   :  Optional[Any]        =					flow_network.graph
       lowercase   :  str        =					False






  def    __a     (    self						:      Optional[int] )						->       Any:






       """simple docstring"""







       if not self.executed:
            self._algorithm()
            lowercase   :  List[Any]        =					True






  def    __a     (    self						:      Optional[Any] )						->       Any:






       """simple docstring"""







       pass


class 		_A   (    _lowerCamelCase ):






  def __init__(    self						:      Any ,		_A						:      List[str] )						->       Optional[int]:






       """simple docstring"""







       super().__init__(_A )
       # use this to save your result
       lowercase   :  str        =					-1






  def    __a     (    self						:      List[str] )						->       int:






       """simple docstring"""







       if not self.executed:
            raise Exception('''You should execute algorithm before using its result!''' )

       return self.maximum_flow


class 		_A   (    _lowerCamelCase ):






  def __init__(    self						:      Union[str, Any] ,		_A						:      Optional[int] )						->       Any:






       """simple docstring"""







       super().__init__(_A )

       lowercase   :  Dict        =					[[0] * self.verticies_count for i in range(self.verticies_count )]

       lowercase   :  Optional[int]        =					[0] * self.verticies_count
       lowercase   :  Union[str, Any]        =					[0] * self.verticies_count






  def    __a     (    self						:      Optional[int] )						->       Optional[int]:






       """simple docstring"""







       lowercase   :  Any        =					self.verticies_count

       # push some substance to graph
       for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index] ):
            self.preflow[self.source_index][nextvertex_index] += bandwidth
            self.preflow[nextvertex_index][self.source_index] -= bandwidth
            self.excesses[nextvertex_index] += bandwidth

       # Relabel-to-front selection rule
       lowercase   :  Optional[int]        =					[
           i
           for i in range(self.verticies_count )
           if i != self.source_index and i != self.sink_index
       ]

       # move through list
       lowercase   :  Union[str, Any]        =					0
       while i < len(_A ):
            lowercase   :  int        =					vertices_list[i]
            lowercase   :  Optional[Any]        =					self.heights[vertex_index]
            self.process_vertex(_A )
            if self.heights[vertex_index] > previous_height:
                 # if it was relabeled, swap elements
                 # and start from 0 index
                 vertices_list.insert(0 ,		vertices_list.pop(_A ) )
                 lowercase   :  Optional[int]        =					0
            else:
                 i += 1

       lowercase   :  Dict        =					sum(self.preflow[self.source_index] )






  def    __a     (    self						:      int ,		_A						:      Tuple )						->       Optional[Any]:






       """simple docstring"""







       while self.excesses[vertex_index] > 0:
            for neighbour_index in range(self.verticies_count ):
                 # if it's neighbour and current vertex is higher
                 if (
                     self.graph[vertex_index][neighbour_index]
                     - self.preflow[vertex_index][neighbour_index]
                     > 0
                     and self.heights[vertex_index] > self.heights[neighbour_index]
                 ):
                      self.push(_A ,		_A )

            self.relabel(_A )






  def    __a     (    self						:      Tuple ,		_A						:      Union[str, Any] ,		_A						:      List[Any] )						->       List[str]:






       """simple docstring"""







       lowercase   :  Optional[Any]        =					min(
           self.excesses[from_index] ,		self.graph[from_index][to_index] - self.preflow[from_index][to_index] ,		)
       self.preflow[from_index][to_index] += preflow_delta
       self.preflow[to_index][from_index] -= preflow_delta
       self.excesses[from_index] -= preflow_delta
       self.excesses[to_index] += preflow_delta






  def    __a     (    self						:      Optional[Any] ,		_A						:      Tuple )						->       Tuple:






       """simple docstring"""







       lowercase   :  List[Any]        =					None
       for to_index in range(self.verticies_count ):
            if (
                self.graph[vertex_index][to_index]
                - self.preflow[vertex_index][to_index]
                > 0
            ) and (min_height is None or self.heights[to_index] < min_height):
                 lowercase   :  List[Any]        =					self.heights[to_index]

       if min_height is not None:
            lowercase   :  List[Any]        =					min_height + 1


if __name__ == "__main__":
 lowerCAmelCase_						 =					[0]
 lowerCAmelCase_						 =					[3]
 # graph = [
 #     [0, 0, 4, 6, 0, 0],
 #     [0, 0, 5, 2, 0, 0],
 #     [0, 0, 0, 0, 4, 4],
 #     [0, 0, 0, 0, 6, 6],
 #     [0, 0, 0, 0, 0, 0],
 #     [0, 0, 0, 0, 0, 0],
 # ]
 lowerCAmelCase_						 =					[[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

 # prepare our network
 lowerCAmelCase_						 =					FlowNetwork(graph, entrances, exits)
 # set algorithm
 flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
 # and calculate
 lowerCAmelCase_						 =					flow_network.find_maximum_flow()

 print(f'''maximum flow is {maximum_flow}''')





'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase_					=   {"configuration_fnet": ["FNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "FNetConfig"]}

try:
  if not is_sentencepiece_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_					=   ["FNetTokenizer"]

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_					=   ["FNetTokenizerFast"]

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_					=   [
      "FNET_PRETRAINED_MODEL_ARCHIVE_LIST",
      "FNetForMaskedLM",
      "FNetForMultipleChoice",
      "FNetForNextSentencePrediction",
      "FNetForPreTraining",
      "FNetForQuestionAnswering",
      "FNetForSequenceClassification",
      "FNetForTokenClassification",
      "FNetLayer",
      "FNetModel",
      "FNetPreTrainedModel",
  ]


if TYPE_CHECKING:
  from .configuration_fnet import FNET_PRETRAINED_CONFIG_ARCHIVE_MAP, FNetConfig

  try:
    if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_fnet import FNetTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_fnet_fast import FNetTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_fnet import (
        FNET_PRETRAINED_MODEL_ARCHIVE_LIST,
        FNetForMaskedLM,
        FNetForMultipleChoice,
        FNetForNextSentencePrediction,
        FNetForPreTraining,
        FNetForQuestionAnswering,
        FNetForSequenceClassification,
        FNetForTokenClassification,
        FNetLayer,
        FNetModel,
        FNetPreTrainedModel,
    )


else:
  import sys

  UpperCAmelCase_					=   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



